Magnet structure for focusing of magnetic resonance images

ABSTRACT

Apparati and methods for magnetic resonance imaging a selected interrogation volume in a tissue of a human or animal body, to provide increased signal-to-noise ratios for fixed data acquisition times. The method involves excitation of magnetic resonance in a selected interrogation volume that may be as small as 500-3,000 cm 3 , through controllable focusing or steering of a rotating magnetic field signal used to induce magnetic resonance. The response signals issued by the excited volume element are then collected by focusing of these response signals, using a phased array of antennae for this purpose. Use of the invention with well known nuclear magnetic resonance excitation procedures, such as spin echo, echo planar, gradient recalled and backprojection, are discussed.

FIELD OF THE INVENTION

This invention relates to medical imaging of a human or animal body, andparticularly of the cardiac region, using RF focusing techniquestogether with nuclear magnetic resonance imaging in high magneticfields, to improve the signal-to-noise ratio per unit data acquisitiontime and to improve the spatial resolution, spectroscopic sensitivityand/or data throughput rate of such imaging.

BACKGROUND OF THE INVENTION

Medical imaging techniques for organs and tissues in a human or animalbody have changed considerably over the last 20 years, in good measurebecause of adoption of nuclear magnetic resonance imaging for medicalimaging. Damadian(Science 171 (1971) 1151-1153), Weisman(Science 178(1972) 1288-1290), Lauterbur(Nature 242(1973) 190-191), Eggelston etal(Cancer Research 33 (1973) 2156-2160) and Damadian et al (Proc. Nat.Acad. Sci. 71 (1974) 1471-1473; Science 194 (1976) 1430-1431) were amongthe first to recognize the value of, and to apply the techniques of, NMRto distinguish between normal and abnormal developments in human andanimal bodies.

Nuclear magnetic resonance ("NMR") is a relatively young research areaand was first discussed and experimentally investigated by Bloch and hisco-workers in 1946 (Phys. Rev. 70 (1946) 460-474 and 474-485). The Blocharticles are incorporated herein by reference. In NMR, an approximatelyconstant magnetic field B₀ =B₀ i_(z) is applied in a fixed direction,which defines the z-axis of the associated coordinate system, to thetarget(organ, tissue, etc.), and a time-varying field B₁ =B₁ (i_(x)cosωt+i_(y) sinωt) is applied in a plane perpendicular to thez-direction, where the amplitude B₁ is also approximately constant. Themagnetic polarization vector M satisfies the magnetization torqueequation

    dM/dt=γ(M×B)+(M.sub.0 /T1)i.sub.z -ΩM    (1)

where γ is the gyromagnetic ratio, B=B₀ +B₁ is the total impressedmagnetic field, M₀ is an equilibrium magnetization established by thepolarization field, T1 is a characteristic time interval for return toequilibrium of the transverse component of magnetization, T2 is acharacteristic time interval describing de-phasing of the magnetization,and Ω is a diagonal second rank tensor or dyadic that phenomenologicallyaccounts for relaxation of the three magnetization components that is ofthe form ##EQU1## For protons, the ratio γ is 42.57 MHz per Tesla. Thespin-lattice relaxation time T1 and the spin-spin relaxation time T2 areoften of the order of 600-1,000 msec and 20-100 msec, respectively. Theobservable quantities are M_(x) and M_(y).

These equations can be solved under various driving and receiving fieldconditions to obtain the magnetization components for the system. Whenthe system is excited by a radiofrequency ("RF") magnetic fieldintensity B₁ at or near the resonant frequency f₀ =ω₀ /2τ=γB₀, the spinsystem will draw energy from the RF exciting field. Conversely, if thespin system is near resonance, energy can be returned to a structurepositioned to receive this RF energy. Analysis of the system ofequations in Eq. (1) is discussed by A. Abragam, The Principles ofNuclear Magnetism, Oxford University Clarendon Press, 1961, pp. 37-75,and is incorporated herein by reference. Medical imaging is concernedgenerally with receipt and interpretation of the fields produced by thisgiven-back energy.

In subsequent discussions, it will be assumed that the frame ofreference is one that rotates with the RF rotating magnetic field B₁ atthe resonant frequency f₀. The magnetization components M_(x), andM_(y), are of particular interest here. In a frame rotating with thefield, the magnetic field directed along the x'-axis in the rotatingframe produces a magnetization only along the y'-axis. In this frame,the broadband RF pulse and various gradient magnetic fields (discussedbelow) that perturb the spin system are easily visualized and analyzed.

One problem that faces any approach to excitation, selective orotherwise, of a tissue, organ or other biological component of a humanor animal body (herein referred to simply as "tissue" for convenience),or parts thereof, is that the "noise", which arises from tissue notwithin the desired volume element, is often substantial because of therelatively large surrounding tissue volume that produces such noise. Atime-varying magnetic field B₁ in the tissue produces a correspondingelectric field E₁ by Maxwell's equations, and because the tissue hasnon-zero conductivity, this produces a corresponding non-zero currentvector J. The volume integral of the scalar product of J and E givesrise to power dissipation in the entire tissue volume element, and thisproduces noise at the signal sensing apparatus unless the field of viewof the tissue volume element can be somehow limited. This process can berepresented by a "body noise" resistor whose contribution isproportional to tissue conductivity. Noise sets a lower limit on theresolution, expressed as the smallest volume of tissue that can besensed by the receiver, and sets a lower limit on the length of the timeinterval over which signal acquisition is possible. Noise is produced byuncontrolled electronic action in the receiver circuits ("Johnsonnoise"), by the "body noise" resistor noise source, and by thermallyinduced magnetization in the tissue being imaged.

Three volume elements, of quite different sizes, are involved here: (1)tissue volume, which can be a few hundred to a few hundred thousand cm³in size; (2) RF signal interrogation volume from which the receiverreceives the sensed response signals; and (3) magnetic resonanceexcitation volume or "voxel volume" within the tissue, which can be muchless than 1 mm³ in size. The interrogation volume is defined by thevolume surrounded by the coil, applicator or other transmitter used togenerate the RF magnetic field and by the extent of the unwantedelectric field generated in the body itself. In conventional approaches,this interrogation volume can be 50,000-100,000 cm³, which is muchlarger than the tissue volume for cardiac monitoring. Preferably, theinterrogation volume should be about the same size as the tissue volume,or smaller.

According to one well known relation in magnetic resonance physics, thesignal-to-noise ratio (SNR) is proportional to the product of B₀ and avolume ratio:

    SNR∝B.sub.0 [voxel volume/interrogation volume][Δt].sup.1/2,

where Δt is the data acquisition time and B₀ is the primary magneticfield strength. Increase of B₀ causes a proportional increase in thesystem's resonant frequency. Increase of Δt is often constrained bythroughput requirements. Increase of B₀ and/or reduction of theinterrogation volume is thus a primary concern, if the signal-to-noiseratio is to be increased.

What is needed here is an approach that (1) minimizes or suppresses thebody noise per unit acquisition time that issues from the tissue volume,and (2) increases the available signal per unit acquisition time.

SUMMARY OF THE INVENTION

These needs are met by the invention which, in one embodiment, providesa method for limiting the field of view, and thus the noisecontribution, by reducing the interrogation volume element to a size nolarger than 3,000 cm³ in a tissue in a human or animal body. The methodprovides for increased signal by use of a primary magnetic field B₀ oflarger magnitude (2-10 Telsa). In order to limit the field of viewwithin the body or tissue, a high frequency RF magnetic field, with f₀=85-340 MHz, is chosen for the rotating field. The corresponding oreffective wavelength λ within the tissue is relatively short (11-41 cm),due to the high dielectric permittivity of tissue at such frequencies.This short effective wavelength allows one to focus the RF energy withina modest size interrogation volume element in the tissue, thus markedlylimiting the field of view.

According to this method, a first or primary magnetic field (intensity)B₀ =B₀ i_(z) is applied in a first (z) direction and a second focusedmagnetic field B₁ (x,y,z,t), sometimes referred to herein as B₁ forconvenience of notation, is applied in a perpendicular (xy) plane, whereB₁ has constant magnitude, rotates in the xy-plane with approximatelyconstant angular frequency ω, and is applied only over a first timeinterval t₁ <t<t₁ +Δt₁ for predetermined quantities t₁ and Δt₁.Application of the field B₁ provides a "theta pulse" that tips themagnetization vector M away from the z-axis toward the xy-plane by apredetermined reorientation angle θ, and two popular choices are θ=90°and θ=10°-20°, as discussed below. For convenience of notation, theprimes on the coordinates x',y',z' in the rotating frame are dropped inthe following discussion.

A slice select gradient magnetic field B₂ (z) is applied to the tissue,either simultaneously with or preceding application of the field B₁, toconvert a portion of the longitudinal magnetization M₀ in a selectedz-slice into xy-plane magnetization M_(x) and/or M_(y) over apredetermined time interval given by t₂ <t<t₂ +Δt₂, where t₂ ≦t₁.

One or more additional gradient magnetic fields e,uns/B/ ₃ (x,y) is thenapplied to put the magnetization in selected tissue voxel volumeelements within the chose z-slice into differential magnetic resonanceover a predetermined time interval, in order to "tag" the (x, y) spatiallocations of these voxels. The gradient magnetic fields B₂ (z) and B₃(x,y) all have field vectors parallel to the field vector of the primarymagnetic field B₀. A "read" cycle is then initiated by application of anRF magnetic field B₅ (x,y,z,t) plus another gradient magnetic field B₆(x,y), or the gradient magentic field B₆ (x,y) alone, to the tissuevoxel volume elements within the z-slice. The magnetization thusproduced excites electromagnetic signals that issue from the selectedtissue voxel volume elements within a determinable time interval givenby t_(sig) <t<t_(sig) +Δt_(sig). The spatial locations of these voxelvolume elements, from which the electromagentic signals issue, are thus"tagged" by the choice of the gradient magnetic fields.

An array of sampling antennae, numbered n=1, 2, . . . , N, which sensesthe direction and amplitude of electromagnetic response signals issuedby the selected nuclei, is provided, where antenna number n in the arrayis activated to sense these signals only over a predetermined timeinterval, given by t_(sig),n <t<t_(sig),n +Δt_(sig),n, that depends uponn. This particular nth time interval corresponds to receipt, an antennanumber n, of the response signal that was issued by the excited selectednuclei in the predetermined time interval t_(sig) <t<t_(sig) +Δt_(sig).Differences among these N time intervals may be compensated for by useof phase shifts, time delays or other similar adjustments in theresponse signals received.

Excitation of magnetization in the selected voxel volume elements can beaccomplished by a number of approaches, including but not limited to thespin echo method, the echo planar method, the gradient recalled method,a backprojection method and various spectroscopic imaging techniques.All of these provide spatially resolved discrimination of thismagnetization.

Selective sensing of the electromagnetic signal issued by the selectednuclei in the voxel volume elements is implemented by an array ofantennae surrounding the tissue volume. The sequence of antennaactivation time intervals t_(sig),n <t<t_(sig),n +Δt_(sig),n is chosenso that the sensing antenna number n is activated and senses thereceived or response signal RS (FID, spin echo or other resultantsignal) that was issued by the selected magnetization in the tissueduring the antenna's own activation time interval t_(sig),n<t<t_(sign),n +Δt_(sig),n, within which it receives this response signalRS. Because the RS signal thus issued by the selected magnetization mayrequire different amounts of time to reach each of the sensing antennaein the array, the times t_(sig),n and/or the time interval lengthsΔt_(sig),n may differ from one antenna to another. If the sensingantennae are arrayed approximately on the circumference of a circle withthe selected voxel volume elements positioned at the center, theparameters t_(sig),n and, separately, the parameters Δt_(sig),n may beapproximately equal within each parameter set. If the sensing antennaeare arrayed on two or more planes adjacent to the tissue theseparameters may be quite different from one another within each parameterset.

The sensing antennae also serve as the source of the transmittedmagnetic field B₁ in one group of embodiments of the invention. Inalternative embodiments, the transmitted magnetic field B₁ is providedby a first array of antennae or other sources and the sensing antennaeform a second, separate array to recover the response signal RS.

In all embodiments, the invention includes apparatus for producingnuclear magnetic resonance in a tissue and for sensing the RS signalsinduced in the selected nuclei in the tissue. In a first embodiment, theapparatus includes a dipolar magnet, excited by current-carrying coils.The magnet substantially surrounds the patient's body and produces anapproximately homogeneous magnetic field of specific field strength inthe range 2-10 Tesla in a first (z) direction in the body. The apparatusincludes an RF magnetic field source that produces a rotating magneticfield with approximately constant magnitude, with the magnetic fieldvector rotating in an xy-plane perpendicular to the z-direction withapproximately constant angular frequency. The apparatus further includesa switched power source for the rotating magnetic field source so thatthis rotating magnetic field can be activated and deactivated duringpredetermined time intervals. The apparatus also has gradient magneticfield means for applying one or more additional gradient magneticfields, over predetermined time intervals, to the tissue to exciteselected magnetization in selected voxel volume elements in the tissue.The apparatus also includes an array of sensing antennae, positioned asa phased array adjacent to the tissue, to sense the RS signals issued bythe selected magnetization. Several embodiments of these arrays areavailable. The apparatus further includes switching means connected toeach sensing antenna to independently activate each antenna over apredetermined time interval so that each antenna senses the RS signalsonly over its own time interval.

Recall that the z-axis of the associated coordinate system is determinedby the direction of the primary magnetic field B₀ and that the magneticfield B₁ (x,y,z,t) rotates in a plane that is perpendicular to thedirection of B₀. A second coordinate system is defined by three distinctplanes relative to the human or animal body being examined: (1) a"transverse plane" TP that is oriented perpendicular to a longitudinalline that runs approximately parallel to the backbone of the body; (2) a"sagittal plane" SP that includes a longitudinal line of the body andincludes a line that passes from the back to the front of the body; and(3) a "coronal plane" CP that includes a longitudinal line of the bodyand includes a line that passes from the right side of the body to theleft side of the body. These three planes are illustrated in FIG. 1 andare defined by the body b itself. A transverse plane, sagittal plane orcoronal plane may pass through the body or be positioned outside andadjacent to the body to which it refers.

In a first embodiment of the phased array of antennae, the primarymagnetic field B₀ is oriented perpendicular to a coronal plane and theRF magnetic field B₁ (x,y,z,t) rotates in this coronal plane. Twoantennae arrays, positioned in coronal planes located in front of andbehind the body, provide an RF magnetic field B₁. In a secondembodiment, the primary magnetic field B₀ and the RF magnetic field B₁are oriented as in the first embodiment, but the RF magnetic field B₁ isproduced by a differently positioned array of antennae, located at theright side and left side of the body. In a third embodiment of thephased array of antennae, the primary magnetic field B₀ is orientedperpendicular to a transverse plane and the RF magentic field B₁ rotatesin this transverse plane. In a fourth embodiment of the phased array ofantennae, the primary magnetic field B₀ is oriented perpendicular to asagittal plane and the RF magnetic field B₁ rotates in the sagittalplane.

In a general embodiment of the method invention, an approximatelystatic, approximately homogeneous, primary magnetic field B₀ oriented ina predetermined (z) direction is applied to the tissue, or to theinterrogation volume of the tissue, and an RF magnetic field B₁(x,y,z,t), which rotates in a plane that is approximately perpendicularto the field vector B₀, is applied over a first predetermined timeinterval given by t₁ <t<t₁ +Δt₁. A slice-select, gradient magentic fieldB₂ (z) is applied over a predetermined time interval given by t₂ <t<t₂+Δt₂, in order to select a particular slice of the tissue. This gradientmagnetic field B₂ (z) is oriented parallel to the primary magnetic fieldB₀ but has much smaller magnitude and varies strictly monotonically withchange in position in the z-direction. One or more additional gradientmagnetic fields B₃ (x,y), with field vector oriented parallel to thez-direction but changing with position in directions x and y in a planeperpendicular to the z-direction, is applied over a predetermined timeinterval given by t₃ <t<t₃ +Δt₃, in order to selectively excite voxelvolumes within the chosen z-slice for study. The selected volume isexcited by another RF rotating magnetic field and another gradientmagnetic field, or by a gradient field alone, and a response signal issensed at one or more phased arrays of antennae. The individual antennaereceive the response signals RS at different times and compensate forthis by means of internal phase shifts, time delays or other adjustmentsat the individual antennae that make up the array; these adjustmentswere used to focus the antenna array on the interrogation volume ofinterest. The resulting signals are then processed in order to properlyanalyze and display the response signals RS produced within theinterrogation volume.

To evaluate and diagnose cardiac and other diseases of the heart andother organs and tissues non-invasively, a device that can image theanatomical structures with sub-millimeter resolution and that can viewbiochemical functions such as perfusion and metabolism withsub-centimeter resolution is provided. Diagnostic magnetic resonanceimaging and spectroscopy, using RF focusing techniques and a highstrength primary magnetic field, provide the improved signal-to-noiseratios that are required to achieve sub-millimeter spatial resolutionand sub-centimeter localized spectroscopic signals. Focusing of thetransmit and receive radiofrequency electromagnetic fields allows thevolume of tissue from which response signals are sensed to be limited toa much smaller interrogation volume of interest, in order to reduce theenergy deposited in the tissue by this radiation. Use of a plurality ofsensing antennae, positioned in a phased array, allows an increase inthe signal to noise ratio and allows a concomitant improvement in thedata acquisition rate for the system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates typical transverse, sagittal and coronal planes of abody.

FIG. 2 is a flow chart illustrating the method invention generally.

FIG. 3 is a schematic view of the magnetic field configuration used inan embodiment of the invention.

FIGS. 4 and 5 illustrate the signal attenuation coefficient andcharacteristic wavelength, respectively, as a function of signalfrequency, for one biological material of interest, canine muscle, ananalog of human tissue.

FIGS. 6A, 7A and 8A are flow charts illustrating the steps in theinvention when used together with the spin echo method (FIG. 6A), theecho planar method (FIG. 7A) and the gradient recalled method (FIG. 8A).

FIGS. 6B, 7B and 8B are graphs illustrating the sequence of magneticfields used in the spin echo approach (FIG. 6B), the echo planarapproach (FIG. 7B) and the gradient recalled approach (FIG. 8B) forselective excitation of a volume element according to the invention.

FIGS. 9A and 9B are front and side view illustrating one embodiment ofthe source of the rotating magnetic field B₁, rotating or oscillating ina coronal plane, and sensing antennae for receipt of the RS signals.

FIGS. 10A and 10B are front and side views illustrating a secondembodiment of the source of the rotating magnetic field B₁, rotating oroscillating in a coronal plane, and sensing antennae for receipt of theRS signals.

FIGS. 11A and 11B are top and end views illustrating a third embodimentof the source of the rotating magnetic field B₁, rotating or oscillatingin a transverse plane, and sensing antennae for receipt of the RSsignals.

FIGS. 12A and 12B are front and side views illustrating a fourthembodiment of the source of the rotating magnetic field B₁, rotating oroscillating in a sagittal plane, and sensing antennae for receipt of theRS signals.

FIG. 13 is a front view illustrating the magnetic field apparatus thatproduces the fields used in implementing the invention shown in FIGS. 9Aand 9B.

FIGS. 14A and 14B are front and top views illustrating an embodiment ofmagnetic field apparatus that produces the magnetic field used inimplementing the invention shown in FIGS. 10A and 10B.

FIGS. 15 (top view) and 16 (front view) illustrate the magnetic fieldapparatus used in implementing the invention shown in FIGS. 11A/11B and12A/12B.

FIG. 17 schematically illustrates the configuration used for focusingsignals transmitted to a target element or for focused receipt of RSsignals issued by the target volume element at the sensing antennae.

FIG. 18 schematically illustrates a configuration that is useful inobtaining focusing of magnetic fields at various positions along a linewithin a body.

FIGS. 19A and 19B are schematic views of an embodiment for mostly-analogsignal processing of the response signals received from the excitedselected nuclei in the interrogation volume.

FIGS. 20A and 20B are schematic views of an embodiment formostly-digital signal processing of the response signals received fromthe excited nuclei in the interrogation volume.

DESCRIPTION OF BEST MODE

FIG. 2 is a flow chart illustrating the general method of the invention.The tissue, identified as 31 in FIG. 3, is placed in a static,homoegeneous primary magentic field B₀, oriented in a first (z)direction in the laboratory frame, in the first step 11. A rotatingmagentic field B₀ (x,y,z,t) is applied in an xy-plane that isapproximately perpendicular to the z-direction in the third step 13. Therotating magnetic field B₁ has approximately constant magnitude androtates with approximately constant angular frequency ω in the xy-plane.The primary and rotating magentic fields may be representedapproximately as

    B.sub.0 =B.sub.0 i.sub.z,                                  (3)

    B.sub.1 (x,y,z,t)=B.sub.1 (x,y,z,t) (i.sub.x cosωt+i.sub.y sinωt),                                             (4)

where i_(x), i_(y) and i_(z) form a mutually orthogonal triad of unitlength vectors, oriented in the x-, y- and z-directions in the rotatingframe, respectively, where the z-direction coincides with the directionof the static primary field B₀. The equations (1)-(4) are most easilyanalyzed in a rotating frame that rotates with the rotating magneticfield B₁ (x,y,z,t), as discussed by Abragam, ibid. A slice-selectgradient magnetic field B₂ (z)=B₂ (z)i_(z) (amplitude varying with acoordinate, here z) is applied to the tissue approximatelysimultaneously with the RF magnetic field B₁, to excite magnetization inselected voxel volume elements 33 in the interrogation volume (FIG. 2,step 12), shown in FIG. 3. The RF magnetic field B₁ (x,y,z,t) is appliedin a time interval given by t1<t<t1+Δt1.

FIG. 3 illustrates the general configuration of the magnetic fields B₀,B₁ and B₂ used to collectively excite magnetization in the selectedslice or volume elements 33 in the tissue 31. The magnetic field vectorB₂ (z) is oriented in the z-direction, with amplitude B₂ (z) increasing(or decreasing) strictly monotonically as the coordinate z increases.The amplitude B₂ (z) may increase linearly with z, as a power law in zwith B₂ (z)∝z^(a) (a≠0), or in some other manner. The range ofamplitudes of this third magnetic field B₂ (z) is chosen so that theconditions for nuclear magnetic resonance are satisfied in a narrowz-slice, given by z₂ <z<z₂ +Δz₂, and this occurs over a predeterminedtime interval given by t₂ <t<t₂ +Δt₂.

Returning to FIG. 3, selective excitation of the selected particles inthe selected voxel volume elements 33 of the tissue 31 is caused tooccur over a predetermined time interval given by t₁ <t<t₁ +Δt₁, with t₂≦t₁, after which external excitation of the selected voxel volumeelements by the field(s) B₁ (x,y,z,t) ceases. In step 15, a timesequence of one or more gradient magnetic fields B₃ (x,y), all withfield vectors oriented in the z-direction, is applied to spatiallyencode the magnetization in the voxel volume elements 33, according to adesired phase shift or resonance frequency perturbation, as a functionof the x- and/or y-coordinates. This occurs over a time interval givenby t₃ <t<t₃ +Δt₃.

Another rotating magnetic field, B₅ (x,y,z,t) (not required in some ofthe approaches discussed below), having the same angular frequency as B₁(x,y,z,t) but applied for a longer time interval or with a greater fieldamplitude, is then applied in step 16 to the tissue, in the presence ofa gradient magnetic field. Magnetization in the voxel volume elementsthat were prepared by application of the preceding magnetic fields willcause issuance of electromagnetic response signals RS, in a timeinterval given by t_(sig) <t<t_(sig) +Δt_(sig) (step 17). These voxelvolume elements will provide the predominant response signals RS. Aphased array of sensing antennae is then provided adjacent to the tissue31 (FIG. 3) to sense the response signals RS issued by the selectivelyexcited nuclei, as indicated at step 19. Each sensing antenna, numberedn=1, 2, . . . , N, in the phased array is activated for a particulartime interval or "sensed window" W_(n), given by t_(sig),n <t<t_(sig),n+Δt_(sig),n, during which the response signals RS produced in theselected interrogation volume element 33 (FIG. 3) in the time intervalt_(sig) <t<t_(sig) +Δt_(sig), arrive at antenna number n. Devices thatprovide controllable phase shifts or time delays of one signal relativeto another, for example, electronically alterable phase shifters ormixers with variable local oscillator phases or time delays, may be usedto controllably alter the signals transmitted by, or received at, thephased array of antennae. This allows focusing of steering of thesignals in the interrogation volume, in a manner well known inpropagation of electromagnetic signals, as part of the signal processingin step 21 in FIG. 2.

The interior of a human or animal body has many organs, tissues, fluidsand other components, each with a characteristic set of materialparameters, such as dielectric and magnetic permittively, electricalconductivity, etc. Analysis of propagation of electromagnetic signalswithin such a body often uses a set of average parameters for purposesof evaluating signal attenuation and other material responses. Here,material response data on canine muscle, obtained from the publicationby E. C. Burdettet et al, "In-Situ Tissue Permittivity at MicrowaveFrequencies: Perspective, Techniques, Results", appearing in MedicalApplications Of Microwave Imaging, ed. by L. E. Larsen, I.E.E.E. Press,New York, 1986, pp. 13-40, were used to determine a suitable resonantfrequency range for NMR imaging in such materials. Analysis of theMaxwell equations in a linear, isotropic, lossy, electromagnetic mediumlends to solutions for the electric and magnetic field amplitudes E andB in one spatial dimension (r) of the form:

    E, B∝exp[-(α+jβ)r+jωt],            (5)

    (α+jβ).sup.2 =-ωμε+jωσμ, (6)

    μ=magnetic permeability in tissue≅μ.sub.0 =4π×10.sup.-7 Henry/meter,                       (7)

    ε=real part of complex dielectric permittivity in tissue, (8)

    σ=electrical conductivity (mho/meter) in tissue,     (9)

    r=spatial coordinate measured in wave propagation direction, (10)

where ε' and σ may be frequently-dependent. Physically realisticsolutions of Eq. (4) are: ##EQU2##

The quantity λ=2π/βserves as an effective wavelength for an undulatingwave in the spatial coordinate r, the quantity v=ω/β serves as the phasevelocity for this wave, and the quantity β'=20 log₁₀ [α] (in dB/cm)serves as an exponential attenuation coefficient for a wave of temporalfrequency f=ω/2π propagating through the material. FIGS. 4 and 5 presentthe results of calculations of α' and λ, using interpolations of theexperimental data of Burdette et al, supra, for 17 frequencies shown inTable 1, ranging from 14.9 MHz to 340.6 MHz. For NMR imaging of protonswith γ=42.57 MHz/Tesla, these 17 frequencies correspond to primarymagnetic field strengths B₀ of 0.35 Tesla to 8 Tesla, as indicated inTable 1. For proton NMR, primary magnetic field strengths B₀ of 3 Teslato 8 Tesla produce wavelengths λ in the range of 11.3 cm (B₀ =8 Tesla)to 30 cm (B₀ =3 Tesla), with corresponding signal attenuationcoefficients α' of 1.95 dB/cm (8 Tesla) down to 1.4 dB/cm (3 Tesla).This is an attractive range of wavelengths λ for NMR imaging of protons,and the corresponding range of signal attenuation coefficients α' isacceptable for path lengths in the body of no more than 20 cm. Thus, forNMR imaging of protons in material such as canine muscle, primary fieldstrengths B₀ =3-8 Tesla, corresponding to resonant frequencies f₀ =γB₀of 127.7 MHz-340.6 MHz, are quite attractive for this purpose. Forstudies in humans or animals, the range of primary magnetic fieldstrengths will be similar, but not necessarily identical, and will covera total range of primary magnetic field strengths B₀ =2-10 Tesla.

                  TABLE 1                                                         ______________________________________                                        Material Parameters For Canine Muscle Versus Frequency                        B0                                                                            (Tesla)                                                                             Frequency α' (dB/cm)                                                                        λ (cm)                                                                       ε'/ε.sub.o                                                         σ (mho/meter)                      ______________________________________                                        0.35  14.9   MHz    0.53    88.2  161  0.72                                   0.5   21.3          0.66    71.6  125  0.75                                   1.0   42.6          0.92    46.6  90.1 0.83                                   1.5   63.9          1.08    36.2  80.2 0.88                                   2.0   85.1          1.21    30.9  73.1 0.88                                   2.5   106.4         1.31    26.4  65.7 0.85                                   3.0   127.7         1.40    23.6  60.2 0.82                                   3.5   149.0         1.47    21.4  56.9 0.81                                   4.0   170.3         1.54    19.6  54.9 0.81                                   4.5   191.6         1.61    18.6  53.6 0.83                                   5.0   234.1         1.67    16.8  52.7 0.85                                   5.5   234.1         1.72    15.7  52.7 0.87                                   6.0   255.4         1.77    14.7  51.5 0.88                                   6.5   276.7         1.82    13.5  51.1 0.90                                   7.0   298.0         1.87    12.7  50.8 0.91                                   7.5   319.3         1.91    12.0  50.5 0.92                                   8.0   340.6         1.95    11.3  50.2 0.93                                   ______________________________________                                    

To form medical images of targets such as organs and tissues within aliving being, magnetic resonance imaging techniques will be used. Adescription of some of these techniques follows. A selected voxel volumeelement of the tissue can be excited in a predetermined time interval byuse of certain time-dependent gradient magentic fields to produce theconditions required for such resonance in, or adjacent to, that volumeelement. One such method, the spin echo method, is discussed by L. E.Crooks in "An Introduction to Magnetic Resonance Imaging", I.E.E.E.Engrg. in Med. and Biol., vol. 4, (1985) pp. 8-15, incorporated hereinby reference, and proceeds as follows.

With reference to FIG. 6A, the tissue to be imaged is prepared byplacing it in a static, approximately homogeneous magentic field B₀ andsimultaneously applying an RF rotating magnetic field B₁ (x,y,z,t) inthe xy-plane and a z-slice select gradient magentic field B₂ (z), whichmay have the form B₂ (z)=G_(z) i_(z) or any other form that ismonotonically increasing in z. The field B₁ is often referred to as a"90° pulse" in the spin echo method.

Another gradient magnetic field B₃ (y) is introduced, with field vectororiented along the z-direction and field strength increasingmonotonically (e.g., linearly) in the y-direction. The range of fieldstrengths of this fourth magnetic field B₃ is chosen so that theconditions for resonance within the z-slice are the same within narrowy-slices given by y3<y<y3+Δy3, and this occurs only over a predeterminedtime interval given by t3<t<t3+Δt3. Each of these narrow y-slices has adifferent characteristic phase shift associated with it because thelocal magnetic field at each voxel volume element is slightly different.This phase shift changes monotonically (e.g., linearly) with change inthe position coordinate y. Another gradient magnetic field B₄ (x) isintroduced, with field vector in the z-direction and field strengthincreasing monotonically (e.g., linearly) in the x-direction. Theconditions for resonance are satisfied within narrow x-slices given byx4<x<x4+Δx4, and this occurs only over a predetermined time intervalgiven by t4<t<t4+∴t4, with t3+Δt3≦t4. The appropriate frequencyassociated with each narrow x-slice changes with change of the positioncoordinate x. The amplitudes B₃ (y) and B₄ (x) of the fourth and fifthgradient magnetic fields are strictly monotonically increasing (ordecreasing) in the indicated coordinates x and y, respectively.

A sixth rotating magnetic field B₅ (x,y,z,t) with longer duration or agreater amplitude than the field B₁, is applied at a predetermined timeT_(E) /2 after application of the fifth magnetic field B₄ (x) and isoften referred to as a "180 degree pulse". Application of the field B₅reverses the sense of increasing phase in the selected nuclei. At adeterminable time T_(E) after application of the field B₁, a responsesignal RS issues from the previously excited selected nuclei within theoriginal z-slice. This response signal is often referred to as a spinecho signal.

The fourth, fifth and sixth magnetic fields are repeatedly applied apredetermined total of M times, with the magnitude of the fourth orphase encode magnetic field |B₃ (y)| being incremented by a fixed amountwith each new repetition. After the fourth, fifth and sixth magneticfields have been applied, response signals RS issue from the selectivelyexcited volume element, and these signals can be sensed by an adjacentphased array of coils or antennae.

The product of the magnitude of the rotating magnetic field B₁ and thetime over which this field is applied is chosen so that themagnetization vector M]is "tipped" from its initial orientation alongthe z-axis by a reorientation or tipping angle θ. The magnetizationvector M lies in the xy-plane after application of the field B₁(x,y,z,t), corresponding to the tipping angle θ=90°. In a similarmanner, the RF field B₅ (x,y,z,t) is chosen to achieve a tipping angleof 180°. The spin echo method, used together with the method of theinvention, is illustrated in a flow chart in FIG. 6A, with the sequenceof magnetic fields applied being illustrated in FIG. 6B. The manifold ofspin echo signals is processed into a useful image using two-dimensionalFourier transforms of response signals RS.

In the echo planar method, first discussed by P. Mansfield and I. L.Pykett in Jour. of Mag. Resonance, vol. 29 (1978) pp. 355-373 andincorporated herein by reference, the rotating RF magnetic field B₁ fora θ=90° pulse and the z-gradient magnetic field B₂ (z) are switched onduring the same time interval, then switched off. FIG. 7A shows in flowchart form the steps followed in this version of the echo planar method.A steady x-gradient magnetic field B₄ (x) is established for a secondtime interval of length 4 m (m=1, 2, 3, . . . ), where τ ispredetermined, and the y-gradient magnetic field B₃ (y) is establishedand periodically reversed during this second time interval, as shown inthe graphical views of the echo planar magnetic pulse sequences in FIG.7B. This sequence may be repeated to improve signal definition, but asingle such sequence allegedly provides all information for atwo-dimensional scan of a slice defined by the z-gradient magnetic fieldB₂ (z). In another version, 180° pulses are provided to produce spinechoes by periodically reversing the x-gradient magnetic field B₄ (x).

The gradient recalled method, illustrated in flow chart form in FIG. 8A,proceeds in a manner similar to that of the spin echo method, with thefollowing differences. First, the amplitude of the slice-select gradientmagnetic field B₂ =B₂ (z,t) is initially positive (or negative) and thenchanges sign before the field disappears, with the time integral of thefield B₂ over the time interval of application being zero. Second, theamplitude of the frequency encode gradient magnetic field B₄ =B₄ (x,t)also changes sign at a predetermined time, and the integral over thetime for which this field is applied is zero. Third, the product of themagnitude of the rotating magnetic field B₁ and the time over which thisfield is applied is such that the magnetization vector is not tipped byθ=90° into the xy-plane, but is tipped by a smaller angle that isusually no more than θ=20°. FIG. 8B illustrates the sequence of magneticfield amplitudes used to implement the invention, when used togetherwith the gradient recalled method. The gradient recalled method isdiscussed by A. Haase et al in "FLASH Imaging. Rapid NMR Imaging UsingLow Flip-Angle Pulses", Jour. of Mag. Resonance, vol. 67 (1986) pp.258-266, which is incorporated herein by reference.

Another useful method is the convolution/backprojection method,discussed by P. D. Lauterbur in "Image Formation by Induced LocalInteractions; Examples Employing Nuclear Magnetic Resonance", Nature,vol. 292 (1973) pp. 190-191, and by L. Axel et al in "LinogramReconstruction for Magnetic Resonance Imaging", I.E.E.E. Trans. inMedical Imaging, vol. 9 (1990) pp. 447-449, incorporated by referenceherein.

FIGS. 9A and 9B illustrate a top view and side view, respectively, ofone embodiment of the source (the "applicator") of the rotating oroscillating RF second magnetic field B₁ (x,y,z,t) according to theinvention. In these figures, the tissue 71 is shown in outline as ahuman form for definiteness, but any other reasonable form could also beused. The primary magnetic field B₀ is oriented perpendicular to thecoronal plane in the top view in FIG. 9A so that the field vector pointsfrom back to front (or from front to back), as shown in FIG. 9B. Theapplicator includes two plates 73 and 75, each containing an array ofopen waveguides, stripline antennae or similar sources ("antennae") thatproduce a focused sum of magnetic fields B₁ that rotates approximatelyin a plane parallel to the applicator plates at approximately constantangular frequency.

The rotating magnetic field B₁ may be replaced in any of the embodimentsdiscussed herein by a magnetic field B₁ '0 that oscillates in a singledirection lying in the rotating plane. For convenient reference, arotating magnetic field B₁ (corresponding to circular polarization) anda uni-directional oscillating magnetic field B₁ ' (corresponding tolinear polarization) will be collectively referred to here as a"rotating magnetic field".

Referring again to FIG. 9A, the two sections 73 and 75 of the applicatormay each have a fluid or solid 77, positioned between the applicatorsection and the other boundary of the tissue 71, that approximatelymatches the average complex impedance of the tissue material at theangular frequency ω applied by the focused rotating magnetic field B₁.This "impedance-matching material" 77 may be water, physiologicalsaline, gels or other suitable material. Alternatively, the tissue 71could be completely immersed in the impedance-matching material, asdiscussed by S. J. Foti et al in "A Water Immersed Phased Array Systemfor Interrogation of Biological Targets", published in MedicalApplications of Medical Imaging, ed. by L. E. Larsen, I.E.E.E. Press,1986, New York, pp. 148-166. Preferably, the applicator sections shouldbe positioned as close to the tissue 71 as possible, within 5 cm thereofor even contacting the target, in order to reduce the signal loss thatoccurs in transmission of an electromagnetic signal between applicatorand tissue 71.

The applicator sections 73 and 75 are connected to a switched powersupply 78 that activates and deactivates the applicator duringpredetermined time intervals, as discussed above. A source of theprimary magnetic field B₀ and of the gradient magnetic fields, alloriented in the same direction as B₀, may be provided as shown in FIGS.13, 14A/14B, 15 and 16 for the respective embodiments shown in FIGS.9A/9B, 10A/10B, 11A/11B and 12A/12B. The source of the gradient magneticfields in FIGS. 9A/9B may be connected to a switched power supply 79that activates and deactivates the gradient magnetic fields duringpredetermined time intervals. The array of antennae that serves assource of the focused rotating magnetic field B₁ may also serve as thearray of focused sensing antennae used to sense the RS signals issued bynuclei in the selected voxel volume elements of the tissue 71. Aplurality of phased transmitters to individually phase shift the signalsB₁ (x,y,z,t) transmitted from the antennae would be required here.

FIGS. 10A and 10B illustrate another embodiment of the applicator, intop view and side view, respectively. The tissue 81 is partly surroundedby two components 83 and 85 of the applicator, both of which areconnected to one or a plurality of switched power sources 88. Theprimary magnetic field B₀ is again perpendicular to the control planeand is directed from back to front, or from front to back, as shown. Thetwo applicator components 83 and 85 together provide a rotating magneticfield B₁ (x,y,z,t) that rotates with approximately constant angularfrequency ω parallel to a coronal plane passing through the tissue fromthe left side to the right side. Optionally, the volume between thetissue 81 and the applicator components 83 and 85 may be filled with animpedance-matching fluid or solid 87 that matches the relevantelectromagnetic properties of the tissue material. A switched powersupply 88 provides power for the rotating magnetic field sources 83 and85. Another switched power source 89 provides power for the gradientfields, whose field vectors are parallel to B₀. Optionally, the sourcesfor the focused magnetic field B₁ may also serve as the sensing antennaefor the RS signals issued by selectively excited nuclei in the selectedvoxel volume elements in the tissue.

FIGS. 11A and 11B illustrate a third embodiment, in top view and endview, respectively, of the applicator according to the invention. Thetissue 91 is surrounded by a plurality of coils or other RF magneticfield sources 93A, 93B, . . . , 93F, 93G, etc. that are part of theapplicator. These sources together produce a focused rotating magneticfield B₁, best shown in the end view in FIG. 11B, that rotates in atransverse plane with approximately constant angular frequency ω.Another magnetic field source (not shown) produces the primary magneticfield B₀ that is oriented perpendicular to this transverse plane in thisembodiment. The sources for the rotating magnetic field B₁ and for thegradient magnetic fields are powered by a plurality of switched powersupplies 98 and a switched power supply 99, respectively. Optionally,the volume between the applicator components and the edge of the tissuemay be filled with an impedance-matching fluid or solid 97, as in theembodiments illustrated in FIGS. 9A, 9B, 10A and 10B. Optionally, thearray of components 93A, 93B, etc. that serve as the sources for thefocused magnetic field B₁ may also serve as sensing antennae for sensingthe RS signals issued by the selectively excited particles in theselected voxel volume elements of the tissue 91.

FIGS. 12A and 12B are top and side views, respectively, of a fourthembodiment of the applicator according to the invention. The tissue 101has two plates 103 and 105, positioned near the front and back surfacesof the patient or tissue, that serve as part of the applicator. Theplates 103 and 105 contain a plurality of antennae that produce afocused magnetic field B₁ that rotates in a sagittal plane within thetissue 101. The primary magnetic field B₀ has is field vector directedperpendicular to this sagittal plane within the tissue. A plurality ofswitched power supplies 108 and 109 provides power for the focusedrotating magnetic field B₁ and for the gradient magnetic fields,respectively, as discussed above. Optionally, an impedance-matchingfluid or solid 107 may fill the volume between the plates 103 and 105and the target 101, as done in the embodiments of the applicator shownin FIGS. 9A, 9B, 10A, 10B, 11A and 11B. Optionally, the plurality ofcoils or other sources contained in the plates 103 and 105 may alsoserve as the sensing antennae for the RS signals issued by theselectively excited nuclei within the selected voxel volume elements ofthe tissue 101.

FIG. 13 illustrates a front view of one embodiment of apparatus usefulin producing the magnetic fields required by the invention shown inFIGS. 9A and 9B. The useful interrogation volume that can be selectivelyexcited by this apparatus, operating at a primary field strength of 2-10Tesla, is about 500-3,000 cm³ but may be made larger if desired. Adipole magnet having a yoke 41 of suitable material is provided with asequence of coils 43a and 43b, preferably superconducting, to producethe primary magnetic field B₀, which is perpendicular to a coronal planein this embodiment. The focused rotating magnetic field is provided by aphased array 44 of antennae, positioned in two coronal planes adjacentto the body or tissue 53, that produce a magnetic field vector B₁(x,y,z,t) that rotates at an approximately constant angular frequency ωin a coronal plane, as seen in top view in FIG. 9A. Power for producingthe magnetic field B₁ is provided by one or a plurality of switchedpower supplies 45. Gradient coils 47, 48 and 49 provide the supplementalmagnetic field or fields B₂,B₃ and/or B₄ for excitation of the selectedvoxel volume elements and are connected to another switched power supply46. An optional pole piece 51 provides flux concentration for theprimary magnetic field B₀. The body or tissue 53 is optionally supportedon a tissue support 55 that can be transported into and out of theprimary field region 57 for the apparatus.

FIGS. 14A and 14B are front and top views of an embodiment of apparatususeful in producing the magnetic fields required by the invention shownin FIGS. 10A and 10B. The apparatus shown in FIGS. 14A and 14B operatesin a manner similar to the apparatus shown in FIG. 13. The primarymagnetic field B₀ is again perpendicular to a control plane in thisembodiment. The focused rotating or other time-dependent magnetic fieldB₁ (x,y,z,t) is provided by a phased array 44' of coils or antennae,positioned in two sagittal planes adjacent to the body or tissue 53,that produce a magnetic field vector B₁ that rotates at an approximatelyconstant angular frequency ω in a coronal plane, as seen in the top viewin FIG. 10A. Power for producing the magnetic field B₁ is provided by aplurality of switched power supplies 45. Gradient coils 47, 48 and 49provide the supplemental magnetic field or fields B₂, B₃ and/or B₄ forexcitation of the selected voxel volume elements and are connected toother switched power supplies 46. An optional pole piece 51 providesflux concentration for the primary magnetic field B₀. The body or tissue53 is optionally supported on a tissue support 55 that can betransported into and out of the primary field region for the apparatus.

Another embodiment is illustrated in the top view of FIG. 15, in whichthe magnetic rolls 43a and 43b produce a primary magnetic field B₀ thatis perpendicular to a transverse plane within the body or tissue 53. Afocused rotating magnetic field B₁ (x,y,z,t) that rotates in thistransverse plane is produced by a circumferential assembly oflongitudinally-oriented coils or antennae 59. This embodimentcorresponds to the applicator embodiment shown in FIGS. 11A and 11B.Power for the rotating and gradient magentic fields comes from switchedpower supplies 45 and 46.

FIG. 16 illustrates an embodiment of the magnetic field apparatus thatis useful in providing the fields used in the embodiment of theapplicator shown in FIGS. 12A and 12B. The coils 43a' and 43b' have beenrotated by 90° from their orientation in FIGS. 13 and 14A to produce aprimary magnetic field B₀ that is perpendicular to a sagittal plane ofthe patient. The sources 47', 48' and 49' of the gradient magneticfields have also been rotated by 90° to produce gradient magentic fieldsparallel to B₀. The focused rotating magnetic field B₁ is provided bythe antennae 44".

FIG. 17 illustrates the desired focusing or steering of excitationsignals transmitted by a linear array of transmitters A₁, A₂, . . . ,A_(N), located at positions that need not be equidistantly spaced. Thedistance of the interrogation volume element S to its perpendicular"foot", indicated as F, on the line containing the linear array oftransmitters is taken to be h, and the distance from the foot F to thenth transmitter A_(n) is taken to be d_(n). The total phase shift ω_(n),including propagation delay for a signal of effective wavelength λ thattravels from the transmitter, through a phase shifter, to an arrayelement A_(n), to the interrogation volume element S, or in the reversedirection, becomes

    ψ.sub.n =2πR.sub.n /λ+φ.sub.n,           (14)

    R.sub.n =[h.sup.2 +d.sub.n.sup.2 ].sup.1/2                 (15)

    φ.sub.n =phase shift introduced internally at transmitter number n. (16)

In order to achieve focusing or steering at the interrogation element S,it is desirable that

    .sup.ψ 1=.sup.ψ 2= . . . =.sup.ψ N (mod 2π), (17)

which can be achieved by arranging that the internal phase shift φ_(n)introduced at the array element A_(n) satisfies the relations

    φ.sub.n -φ.sub.m =(2π/λ)(R.sub.m -R.sub.n)(mod 2π) (m,n=1,2, . . . , N)                                      (18)

If a signal, issued at the interrogation volume element S, is to becoherently received rather than transmitted at an array of antennareceivers, also indicated as A₁, A₂, . . . , A_(N) in FIG. 17, theassociated phase shifts φ'_(m) and φ'_(n) impressed at the receiversA_(m) and A_(n), respectively, should also satisfy Eq. (18). The phaseshifts φ'_(n) (=φ_(n)) for transmission and/or reception for the phasedarray of antennae {A_(n) }, shown in FIG. 17, can be introducedelectronically and will vary with the location of the interrogationvolume element S. However, these phase shifts can also be introduced inthe software used to process signals to be transmitted or received atthe antennae {A_(n) }, and this is the preferred approach for theinvention.

S. J. Foti et al, supra, have discussed provision of a phased array oftransmitters or receivers at frequencies 20 times as high (˜3 GHz) asthose of interest here, with the transmitting or receiving elementsspaced equal distances apart and with the interrogation volume element Seffectively located at infinity (h infinite). The mathematics used withthe invention disclosed here is somewhat more complex because h isfinite, and the same electronic components can be used for bothtransmitting the rotating magnetic field signals B₁ (x,y,z,t) and forsensing the RS signals received from the interrogation volume element Sthat is selectively excited.

FIG. 17 illustrates focusing on the interrogation volume by aone-dimensional array of transmitting and/or receiving elements,arranged along a line LL'. A one-dimensional array of such elements mayalso be positioned along a curvilinear path, such as a circle, ellipse,hyperbola or parabola. More often, use of a two-dimensional array oftransmitting and/or receiving elements is appropriate; and in thisinstance the elements may be positioned at the vertices of: (1) arectangular lattice; (2) a regular hexagonal lattice; (3) an equilateraltriangular lattice; (4) a lattice of non-equilateral triangles; or (5)some other appropriate two-dimensional lattice, on a planar or curvedsurface. The transmitting and/or receiving elements can also be formedas two or more annular arrays of such elements AR1, AR2 and AR3, asshown in FIG. 18, in order to provide focusing of the excitation RFsignals or response signals RS at a position alone a line LL' thatpasses through the body.

In performing magentic resonance imaging by focusing of the selectiveexcitation signal or focused pick-up of the RS signal, use of thegradient magnetic fields allow resolution of structures of the size ofvoxel volumes. Focusing the array of RF signals allows resolution of astructure the size of the interrogation volume. Movement of thetransmitter or receiver plane in an axial direction, as recommended byFoti et al, supra, is not required for three-dimensional selectiveexcitation or signal pick-up according to the invention.

FIG. 19 illustrates one embodiment of a signal processor that can beused to process the response signals RS received by the array ofantennae A_(n) shown in FIG. 17. When the apparatus operates in thereceiver mode, response signals RS1, RS2, RS3, . . . , RSN arrive ontheir respective signal lines at N transmitter/receiver switches T/R1,T/R2, . . . , T/RN and are passed along N receiver path signal lines toN signal amplifiers 201, 202, . . . , 20N, respectively. Thetransmitter/receiver switches T/Rn are used to protect sensitive circuitfrom damage by high power pulses. The output signals that issue fromeach of the N amplifiers 201, 202, . . . , 20N are split and sent alongN signal lines to an assembly of heterodyne receivers 21n-m (n=1, 2, . .. , N; m=1, 2, . . . , M, with M=3 in this example), each with its ownassociated local oscillator ("LO"), 22n-m. Each heterodyne receiver21n-m produces an output signal with much lower output frequency butwith phase angle preserved, after appropriate filtering, and theheterodyne output signals are passed to phase shift devices 21n-m. Thephase shift device 23n-m introduces a controllable phase shift φ_(n),minto the received response signal passing through that phase shiftdevice. Thus, for example, the phase shift devices 2311, 232-1 and 233-1introduce phase shifts φ₁,1, φ₂,1 and φ ₃,1 into the respective outputsignals that issue from these three devices; and these three outputsignals are combined in a summing device 251 whose output signal is thesum of the N input signals RS1, RS2, . . . , RSN, suitably phaseshifted. Alternatively, the phase shift devices 21n-m may be deleted andthe desired phase shifts may be introduced through controllable phaseshifts in the local oscillator signals from the LOs. The phase-shiftedoutput signals from the summing devices 251, 252 and 253 are received byanalog-to-digital converters ("ADCs") 261, 262 and 263, respectively,and the output signals from these ADCs, after appropriatepost-processing, represent a particular physically determinableparameter associated with the interrogation volume of the tissue, suchas density of the selected nuclei, the spin-lattice relaxation time T1,the spin-spin relaxation time T2, a local diffusion constant for a voxelvolume element, or some spectroscopic parameter. Such a physicallydeterminable parameter can be represented as a spatially resolvedquantity. Any parameter associated with a voxel volume element that canbe measured using this approach will be referred to as a "characterizingparameter" here. The embodiment of phased array signal processing may beused with any array of two or more receivers for the response signalsRS.

When the apparatus shown in FIG. 19 is used as a transmitter rather thanas a receiver, a master oscillator ("MO") 280 with a predeterminedoutput signal frequency produces an oscillating output signal that isreceived by each of N phase shift devices 281, 282, . . . , 28N thatintroduce N predetermined phase shifts φ_(1j), φ_(2j), . . . , φ_(Nj)into the MO signal. These phase shifted signals are then directedthrough N signal amplifiers 291, 292, . . . , 29N, the amplified outputsignals are sent through the respective transmitter/receiver switchesT/R1, T/R2, . . . , T/RN, and the transmitter/receiver output signalsare transmitted by the respective antennae A₁, A₂, . . . , A_(N). Thisprocess is repeated for J-1 additional sets of phase shifts φ=φ_(nj)(j=2, . . . , J) to selectively excite J different interrogationvolumes.

The phase shifted antenna output signals are focused on a particularinterrogation volume in this transmitter mode, in order to selectivelyexcite that selected volume. Alternatively, the phase shifts φ_(nj)(n=1, 2, . . . , N) may be deleted and the body or tissue may be bathedin magnetic field radiation, to non-selectively excite the whole body.Selective excitation of an interrogation volume is preferred here, fortwo reasons. First, irradiation of the whole body or tissue should belimited to the specific portion being examined, in order to limit theenergy deposition and consequent heating to that specific portion.Second, indiscriminate excitation of nuclear magnetic resonance in thebody as a whole will produce undesired response signals from regionsthat are of no interest, and these unwanted response signals must befiltered or otherwise cancelled in order to examine the response signalsfrom the interrogation volume of interest.

Additional computer processing, including signal storage, computation oftwo-dimensional Fourier transforms and other image processing in amemory and Fourier transform module 271 is optionally provided tocomplete the signal processing. A suitable image display 273 may also beprovided to visually display the processed images.

The signals configuration of FIG. 19 is useful if the phase shiftdevices 23n-m and the summing devices 25m are relatively inexpensive andif most of the processing is to be done for signals in analog form. If,on the other hand, most of the processing is to be done for signals indigital form, or if a phase shift device or signal summing device isrelatively expensive, another configuration, shown in FIG. 20, may beused for processing of the response signals RS. In the receiver mode,the response signals RS1, RS2, . . . , RSN arrive at the respectiveantennae A₁, A₂, . . . , A_(N) and are sent along their respectivesignal output lines to signal amplifiers 301, 302, . . . , 30N,respectively. The amplified response signals RS1, RS2, . . . , RSN arereceived and processed by heterodyne receivers 311, 312, . . . , 31N andtheir associated local oscillators 321, 322, . . . , 32N, respectively,to reduce the effective carrier frequencies to the dc-to-kHz range. Theheterodyne receiver output signals are passed through ADCs 331, 332, . .. , 33N, respectively. The output signals of the ADSc 331, 332, . . . ,33N are received by memory modules 341, 342, . . . , 34N, respectively,of a memory unit. The memory module 341 receives and temporarily storesa sequence of samples of the response signal RS1, taken at differenttimes, for subsequent processing. In a similar manner, the memorymodules 34n (n=2, 3, . . . , N) each receive and temporarily store asequence of samples of the response signal RSn.

A first sequence of phase shifts φ=φ_(n),1 (n=1, 2, . . . , N) isdetermined and loaded into phase shift compensation devices 35n that maybe part of the memory units 34n, and each sequence of response signalsamples RSn held in memory modules 34n is sent through the phase shiftcompensation device 35n to impress a selected phase shift φ=φ_(n),1 or acorresponding time delay on that sequence. Alternatively, these phaseshifts can be impressed on the response signals RSn being processed bydeleting the phase shift compensation devices 35n and introducing thedesired phase shifts through controllable phase shifts in the localoscillator signals. The phase-shifted output signals are then sent to asignal summing device 361, and a first sum signal OS1 issues thatrepresents a magnetic resonance response signal received from a firstselected interrogation volume. This process is repeated with J-1additional sets of determined phase shifts φ=φ_(nj) (j=2, 3, . . . , J;n=1, 2, . . . , N) to produce J-1 additional sum signals OSj,representing J-1 other selected interrogation volumes. The collection ofsum signals OS1, OS2, . . . , OSJ represents the response signals issuedby the different selected interrogation volumes. Note that, beyond thememory unit, signal processing may be done "off-line" because theresponse signal samples are fixed in the memory modules. The signalprocessing embodiment shown in FIG. 20 allows off-line signalprocessing, requires only N phase shift devices 35n and one signal sumdevice 361 to be provided for the processing, and allows most of theprocessing to be performed on the signals in digital form. If theresponse signals RS are to be phase shifted and processed in parallel,the entire signal processing module 367 shown in FIG. 20 may bereproduced a suitable number of times and these signal processingmodules may be operated simultaneously to produce the desired images ofthe interrogation volumes.

Operating in the transmitter mode, the apparatus of FIG. 20 begins withan oscillatory signal produced by a master oscillator 370 and deliversthe MO output signal to an array of phase shift devices 371, 372, . . ., 37N that impresses a first sequence of predetermined phase shiftsφ'_(n),1 on these output signals. The phase shifted MO output signalsare amplified by a power amplifier 38n and are then passed to therespective antennae A₁, A₂, . . . , A_(N) for transmission as a focusedbeam. This process continues for each sequence of chosen transmissionphase shifts φ'=φ'_(nj) (n=1, 2, . . . , N; j=1, 2, . . . , J) with eachsuch sequence of phase shifts causing the transmitted magnetic fieldsignals to focus on a selected interrogation volume. Again, if the bodyor tissue is to be uniformly bathed in the rotating magnetic fieldsignal, the phase shift devices 371, 372, . . . , 37N may be deleted.

I claim:
 1. Apparatus for producing a magnetic field for producing andsensing nuclear magnetic resonance within a resolution volume of reducedsize no larger than 1 mm³ in a patient, the apparatus comprising:astatic magnetic field source that produces an approximately spatiallyhomogeneous, static magnetic field of field strength in the range 2-10Tesla with a magnetic field direction in a first, predeterminedcoordinate direction z, the dipole magnet having a gap of sufficientsize to allow a patient, or a portion thereof, to be placed in the gapand within this magnetic field, and the magnet having a plurality ofcoils surrounding portions of the magnet to produce the desired magneticfield; a radiofrequency magnetic field source that produces in thepatient a magnetic field with a field direction that rotates with apredetermined angular frequency ω that is not greater than 426 MHz in arotational plane that is approximately perpendicular to the direction ofthe spatially homogeneous magentic field, with the radiofrequency sourcebeing operated to produce a magnetic field sum that is focused within aselected interrogation volume of size no larger than 3000 cm³ within thepatient during a first selected time interval t₁ ≦t≦t₁ +Δt₁ ; a firstgradient magnetic field source that produces a first gradient magneticfield that is approximately parallel to the static magnetic field andhaving an amplitude that varies strictly monotonically with change ofposition in the coordinate direction z, this first gradient magneticfield being non-zero only over a second selected time interval t₂ ≦t≦t₂+Δt₂, where t₂ <t₁ and t₂ +Δt₂ ≧t₁ +Δt₁ ; a second gradient magneticfield source that produces a second gradient magnetic field that isapproximately parallel to the static magnetic field and having anamplitude that varies monotonically with change of position in a secondcoordinate direction x that is perpendicular to the coordinate directionz, this second gradient magnetic field being non-zero only over a thirdselected time interval t₃ ≦t≦t₃ +Δt₃, where t₁ ≦t₃ and t₃ +Δt₃ ≦t₁ +Δt₁; a third gradient magnetic field source that produces a third gradientmagentic field that is approximately parallel to the static magneticfield and having an amplitude that varies monotonically with change ofposition in a third coordinate direction x that is perpendicular to thecoordinate directions z and x, this third gradient magnetic field beingnon-zero only over a fourth selected time interval t₄ ≦t≦t₄ +Δt₄, wheret₃ ≦t₄ and t₄ +Δt₄ ≦t₁ +Δt₁, where the first, second and third gradientfields are chosen to define a resolution volume for the sum of thestatic, first gradient, second gradient and third gradient magneticfields that is no larger than 1 mm³ ; a power source connected to thestatic magnetic field source, for producing the static magnetic field; aswitched power source, connected to the radiofrequency magnetic fieldsource and to the first, second and third gradient magnetic fieldsources, to activate and deactivate these magnetic field sources duringthe first, second, third and fourth selected time intervals,respectively; a phased array of at least first and second sensingantennae, positioned adjacent to and outside the patient, to sense firstand second electromagnetic response signals, respectively, issued byselectively excited nuclei within the resolution volume, in response toapplication of a combination of the spatially homogeneous, gradient andradiofrequency magnetic fields within the resolution volume; and signalprocessing means for receiving the electromagnetic signals sensed byeach of the sensing antennae, for introducing a predetermined phaseshift in each of these electromagnetic signals relative to one another,and for constructing a representation of a characterizing parameter ofthe selected nuclei contained in the resolution volume in the patient.2. The apparatus of claim 1 wherein said first directions of saidhomogeneous and gradient magnetic fields are perpendicular to a selectedplane with said patient and said radiofrequency magnetic fields rotatewithin this selected plane, where the selected plane is drawn from agroup consisting of a coronal plane, a sagittal plane and a transverseplane for said patient.
 3. The apparatus of claim 1, wherein said signalprocessing means comprises:first and second amplifiers, positioned toreceive first and second response signals that have been received atsaid first and second sensing antenna, respectively, and to form andissue first and second amplified response signals as output signals;first and second local oscillators for producing and issuing first andsecond local oscillator signals of predetermined frequencies; first andsecond heterodyne receivers for receiving the first and second amplifiedresponse signals from the first and second amplifiers, respectively, forreceiving the first and second local oscillator signals, for forming andissuing a first product signal that is a product of the first amplifiedresponse signal and the first local oscillator signal, and for formingand issuing a second product signal that is a product of the secondamplified response signal and the second local oscillator signal; firstand second phase shift means for receiving the first product signal, forintroducing predetermined first and second phase shifts, respectively,in the first product signal, and for issuing these phase shifted signalsas first and second phase shift means output signals; third and fourthphase shift means for receiving the second product signal, forintroducing predetermined third and fourth phase shifts, respectively,in the second product signal, and for issuing these phase shiftedsignals as third and fourth phase shift means output signals; a firstsignal summing device, positioned to receive and form the sum of thefirst and third phase shift means output signals and to issue this sumas a first summing device output signal; a second signal summing device,positioned to receive and form the sum of the second and fourth phaseshift means output signals and to issue this sum as a second summingdevice output signal; and first and second analog-to-digital converterspositioned to receive the first and second summing device outputsignals, respectively, to convert these signals to digital signals, andto issue these converted signals as first and second converter outputsignals.
 4. The apparatus of claim 3, wherein said signal processingmeans further comprises:signal storage means for receiving and storingsaid first and second summing device output signals; transform means forforming and issuing a two-dimensional Fourier transform of said firstsumming device output signal and for forming and issuing atwo-dimensional Fourier transform signal of said second summing deviceoutput signal; and display means for receiving and graphicallydisplaying the Fourier transform signals issued by the transform means.5. The apparatus of claim 1, wherein said signal processing meanscomprises:first and second amplifiers, positioned to receive first andsecond response signals that have been received at said first and secondsensing antenna, respectively, and to issue amplified first and secondresponse signals as output signals; first and second local oscillatorsfor producing and issuing first and second local oscillator signals ofpredetermined frequencies; first and second heterodyne receivers forreceiving the first and second amplified response signals from the firstand second amplifiers, respectively, for receiving the first and secondlocal oscillator signals, for forming and issuing a first product signalthat is a product of the first amplified response signal and the firstlocal oscillator signal, and for forming and issuing a second productsignal that is a product of the second amplified response signal and thesecond local oscillator signal; first and second analog-to-digitalconverters positioned to receive the first and second product signals,respectively, to convert these signals to digital signals, and to issuethese converted signals as first and second converter output signals;first and second memory means for receiving and storing said first andsecond converter output signals, respectively, as first and second timedsequences of samples of said first and second converter output signalsand for issuing these first and second sequences of converter outputsignal samples upon demand; first and second phase shift means forreceiving the first and second sequences of converter output signalsamples from the first and second memory means, respectively, forintroducing predetermined first and second phase shifts, respectively,in the first and second sequences, for issuing these phase shiftedsignal sequences as first and second phase shift output signals, forintroducing predetermined third and fourth phase shifts, respectively,in the first and second sequences of converter output signal samples,and for issuing these phase shifted signal sequences as third and fourthphase shift output signals; and a signal summing device, positioned toreceive and form the sum of the first and second phase shift outputsignals, to issue this first sum as a first summing device outputsignal, representing the response signal issued from a selected firstresolution volume, to receive and form the sum of the third and fourthphase shift output signals, and to issue this second sum as a secondsumming device output signal representing the response signal issuedfrom a selected second resolution volume.
 6. The apparatus of claim 5,wherein said signal processing means further comprises:signal storagemeans for receiving and storing said first and second summing deviceoutput signals; transform means for forming and issuing atwo-dimensional Fourier transform of said first summing device outputsignal and for forming and issuing a two-dimensional Fourier transformsignal of said second summing device output signal; and display meansfor receiving and graphically displaying the Fourier transform signalsissued by the transform means.
 7. The apparatus of claim 1, furthercomprising signal steering means, connected to said plurality ofradiofrequency magnetic field sources, for controllably varying theposition of said resolution volume within said patient.
 8. Apparatus forproducing a magnetic field for producing and sensing nuclear magneticresonance within a resolution volume of reduced size no larger than 1mm³ in a patient, the apparatus comprising:a static magnetic fieldsource that produces an approximately spatially homogeneous, staticmagnetic field of field strength in the range 2-10 Tesla with a magneticfield direction in a first, predetermined coordinate direction z, thedipole magnet having a gap of sufficient size to allow a patient, or aportion thereof, to be placed in the gap and within this magnetic field,and the magnet having a plurality of coils surrounding portions of themagnet to produce the desired magnetic field; a radiofrequency magneticfield source that produces in the patient a magnetic field with a fielddirection that rotates with a predetermined angular frequency ω that isno greater than 426 MHz in a rotation plane that is approximatelyperpendicular to the direction of the spatially homogeneous magneticfield, with the radiofrequency source being operated to produce amagnetic field sum that is focused within a selected interrogationvolume of size no larger than 3000 cm³ within the patient during a firstselected time interval t₁ ≦t≦t₁ +Δt₁ ; a first gradient magnetic fieldsource that produces a first gradient magnetic field that isapproximately parallel to the static magnetic field and having anamplitude that varies strictly monotonically with change of position inthe coordinate direction z, this first gradient magnetic field beingnon-zero only over a second selected time interval t₂ ≦t≦t₂ +Δt₂, wheret₂ <t₁ and t₂ +Δt₂ ≧t₁ +Δt₁ ; a second gradient magnetic field sourcethat produces a second gradient magnetic field that is approximatelyparallel to the static magnetic field and having an amplitude thatvaries monotonically with change of position in a second coordinatedirection x that is perpendicular to the coordinate direction z, thissecond gradient magnetic field being non-zero only over a third selectedtime interval t₃ ≦t≦t₃ +Δt₃, where t₁ ≦t₃ and t₃ +Δt₃ ≦t₁ +Δt₁, wherethe integral with respect to time of the amplitude of this secondgradient magnetic field over the time interval t₃ ≦t≦t₃ +Δt₃ isapproximately zero; a third gradient magnetic field source that producesa third gradient magentic field that is approximately parallel to thestatic magnetic field and having an amplitude that varies monotonicallywith change of position in a third coordinate direction x that isperpendicular to the coordinate directions z and x, this third gradientmagnetic field being non-zero only over a fourth selected time intervalt₄ ≦t≦t₄ +Δt₄, where t₄ ≦t₄ and t₄ +Δt₄ ≦t₃ +Δt₃, where the first,second and third gradient fields are chosen to define a resolutionvolume for the sum of the static, first gradient, second gradient andthird gradient magnetic fields that is no larger than 1 mm³ ; a powersource connected to the static magnetic field source, for producing thestatic magnetic field; a switched power source, connected to theradiofrequency magnetic field source and to the first, second and thirdgradient magnetic field sources, to activate and deactivate thesemagnetic field sources during the first, second, third and fourthselected time intervals, respectively; a phased array of at least firstand second sensing antennae, positioned adjacent to and outside thepatient, to sense first and second electromagnetic response signals,respectively, issued by selectively excited nuclei within the resolutionvolume, in response to application of a combination of the spatiallyhomogeneous, gradient and radiofrequency magnetic fields within theresolution volume; and signal processing means for receiving theelectromagnetic signals sensed by each of the sensing antennae, forintroducing a predetermined phase shift in each of these electromagneticsignals relative to one another, and for constructing a representationof a characterizing parameter of the selected nuclei contained in theresolution volume in the patient.
 9. The apparatus of claim 7 whereinsaid field directions of said homogeneous and gradient magnetic fieldsare perpendicular to a selected plane within said patient and saidradiofrequency magnetic fields rotate within this selected plane, wherethe selected plane is drawn from a group consisting of a coronal plane,a sagittal plane and a transverse plane for said patient.
 10. Theapparatus of claim 8, wherein said signal processing meanscomprises:first and second amplifiers, positioned to receive first andsecond response signals that have been received at said first and secondsensing antenna, respectively, and to form and issue first and secondamplified response signals as output signals; first and second localoscillators for producing and issuing first and second local oscillatorsignals of predetermined frequencies; first and second heterodynereceivers for receiving the first and second amplified response signalsfrom the first and second amplifiers, respectively, for receiving thefirst and second local oscillator signals, for forming and issuing afirst product signal that is a product of the first amplified responsesignal and the first local oscillator signal, and for forming andissuing a second product signal that is a product of the secondamplified response signal and the second local oscillator signal; firstand second phase shift means for receiving the first product signal, forintroducing predetermined first and second phase shifts, respectively,in the first product signal, and for issuing these phase shifted signalsas first and second phase shift means output signals; third and fourthphase shift means for receiving the second product signal, forintroducing predetermined third and fourth phase shifts, respectively,in the second product signal, and for issuing these phase shiftedsignals as third and fourth phase shift means output signals; a firstsignal summing device, positioned to receive and form the sum of thefirst and third phase shift means output signals and to issue this sumas a first summing device output signal; a second signal summing device,positioned to receive and form the sum of the second and fourth phaseshift means output signals and to issue this sum as a second summingdevice output signal; and first and second analog-to-digital converterspositioned to receive the first and second summing device outputsignals, respectively, to convert these signals to digital signals, andto issue these converted signals as first and second converter outputsignals.
 11. The apparatus of claim 10, wherein said signal processingmeans further comprises:signal storage means for receiving and storingsaid first and second summing device output signals; transform means forforming and issuing a two-dimensional Fourier transform of said firstsumming device output signal and for forming and issuing atwo-dimensional Fourier transform signal of said second summing deviceoutput signal; and display means for receiving and graphicallydisplaying the Fourier transform signals issued by the transform means.12. The apparatus of claim 8, wherein said signal processing meanscomprises:first and second amplifiers, positioned to receive first andsecond response signals that have been received at said first and secondsensing antenna, respectively, and to issue amplified first and secondresponse signals as output signals; first and second local oscillatorsfor producing and issuing first and second local oscillator signals ofpredetermined frequencies; first and second heterodyne receivers forreceiving the first and second amplified response signals from the firstand second amplifiers, respectively, for receiving the first and secondlocal oscillator signals, for forming and issuing a first product signalthat is a product of the first amplified response signal and the firstlocal oscillator signal, and for forming and issuing a second productsignal that is a product of the second amplified response signal and thesecond local oscillator signal; first and second analog-to-digitalconverters positioned to receive the first and second product signals,respectively, to convert these signals to digital signals, and to issuethese converted signals as first and second converter output signals;first and second memory means for receiving and storing said first andsecond converter output signals, respectively, as first and second timedsequences of samples of said first and second converter output signalsand for issuing these first and second sequences of converter outputsignal samples upon demand; first and second phase shift means forreceiving the first and second sequences of converter output signalsamples from the first and second memory means, respectively, forintroducing predetermined first and second phase shifts, respectively,in the first and second sequences, for issuing these phase shiftedsignal sequences as first and second phase shift output signals, forintroducing predetermined third and fourth phase shifts, respectively,in the first and second sequences of converter output signal samples,and for issuing these phase shifted signal sequences as third and fourthphase shift output signals; and a signal summing device, positioned toreceive and form the sum of the first and second phase shift outputsignals, to issue this first sum as a first summing device outputsignal, representing the response signal issued from a selected firstresolution volume, to receive and form the sum of the third and fourthphase shift output signals, and to issue this second sum as a secondsumming device output signal representing the response signal issuedfrom a selected second resolution volume.
 13. The apparatus of claim 12,wherein said signal processing means further comprises:signal storagemeans for receiving and storing said first and second summing deviceoutput signals; transform means for forming and issuing atwo-dimensional Fourier transform of said first summing device outputsignal and for forming and issuing a two-dimensional Fourier transformsignal of said second summing device output signal; and display meansfor receiving and graphically displaying the Fourier transform signalsissued by the transform means.
 14. The apparatus of claim 8, furthercomprising signal steering means, connected to said plurality ofradiofrequency magnetic field sources, for controllably varying theposition of said resolution volume within said patient.
 15. Theapparatus of claim 8, wherein said radiofrequency magnetic field sourceproduces in the patient a second radiofrequency magnetic field with afield direction that rotates with said predetermined angular frequency ωin a rotation plane that is approximately perpendicular to saiddirection of said spatially homogeneous magnetic field, with the secondradiofrequency source being operated to produce a magnetic field sumthat is focused within said selected interrogation volume within thepatient during a first selected time interval t₅ ≦t≦t₅ +Δt₅, where t₅>t₂ +Δt₂.
 16. Apparatus for producing a magnetic field for producing andsensing nuclear magnetic resonance within a resolution volume of reducedsize no larger than 1 mm³ in a patient, the apparatus comprising:astatic magnetic field source that produces an approximately spatiallyhomogeneous, static magnetic field of field strength in the range 2-10Tesla with a magnetic field direction in a first, predeterminedcoordinate direction z, the dipole magnet having a gap of sufficientsize to allow a patient, or a portion thereof, to be placed in the gapand within this magnetic field, and the magnet having a plurality ofcoils surrounding portions of the magnet to produce the desired magneticfield; a radiofrequency magnetic field source that produces in thepatient a magnetic field with a field direction that rotates with apredetermined angular frequency ω that is not greater than 426 MHz in arotational plane that is approximately perpendicular to the direction ofthe spatially homogeneous magentic field, with the radiofrequency sourcebeing operated to produce a magnetic field sum that is focused within aselected interrogation volume of size no larger than 3000 cm³ within thepatient during a first selected time interval t₁ ≦t≦t₁ +Δt₁ ; a firstgradient magnetic field source that produces a first gradient magneticfield that is approximately parallel to the static magnetic field andhaving an amplitude that varies strictly monotonically with change ofposition in the coordinate direction z, this first gradient magneticfield being non-zero only over a second selected time interval t₂ ≦t≦t₂+Δt₂, where t₂ <t₁ and t₂ +Δt₂ ≧t₁ +Δt₁ ; a second gradient magneticfield source that produces a second gradient magnetic field that isapproximately parallel to the static magnetic field and having anamplitude that varies monotonically with change of position in a secondcoordinate direction x that is perpendicular to the coordinate directionz, this second gradient magnetic field being non-zero only over a thirdselected time interval t₃ ≦t≦t₃ +Δt₃, where t₁ <t₃ and t₃ +Δt₃ >t₁ +Δt₁; a third gradient magnetic field source that produces a third gradientmagentic field that is approximately parallel to the static magneticfield and having an amplitude that varies monotonically with change ofposition in a third coordinate direction x that is perpendicular to thecoordinate directions z and x, this third gradient magnetic field beingnon-zero only over a fourth selected time interval t₄ ≦t≦t₄ +Δt₄, wheret₃ ≦t₄ and t₄ +Δt₄ ≦t₁ +Δt₁, where the integral with respect to time ofthe amplitude of the third gradient magnetic field over the timeinterval t₄ ≦t≦t₄ 'Δt₄ is approximately zero, where the first, secondand third gradient fields are chosen to define a resolution volume forthe sum of the static, first gradient, second gradient and thirdgradient magnetic fields that is no larger than 1 mm³ ; a power sourceconnected to the static magnetic field source, for producing the staticmagnetic field; a switched power source, connected to the radiofrequencymagnetic field source and to the first, second and third gradientmagnetic field sources, to activate and deactivate these magnetic fieldsources during the first, second, third and fourth selected timeintervals, respectively; a phased array of at least first and secondsensing antennae, positioned adjacent to and outside the patient, tosense first and second electromagnetic response signals, respectively,issued by selectively excited nuclei within the resolution volume, inresponse to application of a combination of the spatially homogeneous,gradient and radiofrequency magnetic fields within the resolutionvolume; and signal processing means for receiving the electromagneticsignals sensed by each of the sensing antennae, for introducing apredetermined phase shift in each of these electromagnetic signalsrelative to one another, and for constructing a representation of acharacterizing parameter of the selected nuclei contained in theresolution volume in the patient.
 17. The apparatus of claim 16 whereinsaid field directions of said homogeneous and gradient magnetic fieldsare perpendicular to a selected plane within said patient and saidradiofrequency magnetic fields rotate within this selected plane, wherethe selected plane is drawn from a group consisting of a coronal plane,a sagittal plane and a transverse plane for said patient.
 18. Theapparatus of claim 16, wherein said signal processing meanscomprises:first and second amplifiers, positioned to receive first andsecond response signals that have been received at said first and secondsensing antenna, respectively, and to form and issue first and secondamplified response signals as output signals; first and second localoscillators for producing and issuing first and second local oscillatorsignals of predetermined frequencies; first and second heterodynereceivers for receiving the first and second amplified response signalsfrom the first and second amplifiers, respectively, for receiving thefirst and second local oscillator signals, for forming and issuing afirst product signal that is a product of the first amplified responsesignal and the first local oscillator signal, and for forming andissuing a second product signal that is a product of the secondamplified response signal and the second local oscillator signal; firstand second phase shift means for receiving the first product signal, forintroducing predetermined first and second phase shifts, respectively,in the first product signal, and for issuing these phase shifted signalsas first and second phase shift means output signals; third and fourthphase shift means for receiving the second product signal, forintroducing predetermined third and fourth phase shifts, respectively,in the second product signal, and for issuing these phase shiftedsignals as third and fourth phase shift means output signals; a firstsignal summing device, positioned to receive and form the sum of thefirst and third phase shift means output signals and to issue this sumas a first summing device output signal; a second signal summing device,positioned to receive and form the sum of the second and fourth phaseshift means output signals and to issue this sum as a second summingdevice output signal; and first and second analog-to-digital converterspositioned to receive the first and second summing device outputsignals, respectively, to convert these signals to digital signals, andto issue these converted signals as first and second converter outputsignals.
 19. The apparatus of claim 18, wherein said signal processingmeans further comprises:signal storage means for receiving and storingsaid first and second summing device output signals; transform means forforming and issuing a two-dimensional Fourier transform of said firstsumming device output signal and for forming and issuing atwo-dimensional Fourier transform signal of said second summing deviceoutput signal; and display means for receiving and graphicallydisplaying the Fourier transform signals issued by the transform means.20. The apparatus of claim 16, wherein said signal processing meanscomprises:first and second amplifiers, positioned to receive first andsecond response signals that have been received at said first and secondsensing antenna, respectively, and to issue amplified first and secondresponse signals as output signals; first and second local oscillatorsfor producing and issuing first and second local oscillator signals ofpredetermined frequencies; first and second heterodyne receivers forreceiving the first and second amplified response signals from the firstand second amplifiers, respectively, for receiving the first and secondlocal oscillator signals, for forming and issuing a first product signalthat is a product of the first amplified response signal and the firstlocal oscillator signal, and for forming and issuing a second productsignal that is a product of the second amplified response signal and thesecond local oscillator signal; first and second analog-to-digitalconverters positioned to receive the first and second product signals,respectively, to convert these signals to digital signals, and to issuethese converted signals as first and second converter output signals;first and second memory means for receiving and storing said first andsecond converter output signals, respectively, as first and second timedsequences of samples of said first and second converter output signalsand for issuing these first and second sequences of converter outputsignal samples upon demand; first and second pulse shift means forreceiving the first and second sequences of converter output signalsamples from the first and second memory means, respectively, forintroducing predetermined first and second phase shifts, respectively,in the first and second sequences, for issuing these phase shiftedsignal sequences as first and second phase shift output signals, forintroducing predetermined third and fourth phase shifts, respectively,in the first and second sequences of converter output signal samples,and for issuing these phase shifted signal sequences as third and fourthphase shift output signals; and a signal summing device, positioned toreceive and form the sum of the first and second phase shift outputsignals, to issue this first sum as a first summing device outputsignal, representing the response signal issued from a selected firstresolution volume, to receive and form the sum of the third and fourthphase shift output signals, and to issue this second sum as a secondsumming device output signal representing the response signal issuedfrom a selected second resolution volume.
 21. The apparatus of claim 20,wherein said signal processing means further comprises:signal storagemeans for receiving and storing said first and second summing deviceoutput signals; transform means for forming and issuing atwo-dimensional Fourier transform of said first summing device outputsignal and for forming and issuing a two-dimensional Fourier transformsignal of said second summing device output signal; and display meansfor receiving and graphically displaying the Fourier transform signalsissued by the transform means.
 22. The apparatus of claim 16, furthercomprising signal steering means, connected to said plurality ofradiofrequency magnetic field sources, for controllably varying theposition of said resolution volume within said patient.